Problem: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{p^2 + 3p - 4}{p^2 - 1}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 3p - 4}{p^2 - 1} = \dfrac{(p + 4)(p - 1)}{(p + 1)(p - 1)} $ Notice that the term $(p - 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p - 1)$ gives: $n = \dfrac{p + 4}{p + 1}$ Since we divided by $(p - 1)$, $p \neq 1$. $n = \dfrac{p + 4}{p + 1}; \space p \neq 1$